A ball is thrown straight out at 80 feet per second from an upstairs window that's 15 feet off the ground. It turns out that its motion can be broken down into its motion in the x-direction (horizontally) and its motion in the y-direction (vertically), and that those two components can be thought of completely independently. In other words, its horizontal motion has no influence on its vertical motion, and vice versa. The two component functions here: x(t)is its position in the x-direction,and y(t) is its position in the y-direction. Which of the following choices is correct?

Question

anonymous · Answer

(Ignore air resistance.) NOTE: Use a reference frame that makes all positions (x and y-coordinates) of the projectile positive.

anonymous · Answer

x(t) = 80t, y(t) = 15-16t^2
x(t) = 15 - 16t^2, y(t) = 80t
x(t) = 80t - 16t^2, y(t) = 15
x(t) = 80sint, y(t) = 15 - 16t^2 + 80cost
x(t) = 80t, y(t) - 16t^2

ddcamp · Answer

If there's no air resistance, then there are no forces acting in the x direction, so x-velocity is constant (x(t) is linear)

The y position is a quadratic. The initial y-position is 15ft, so there will be  +15 somewhere in the equation. There is no initial y-velocity, so there will be no t-term, just a t² term

anonymous · Answer

Based on your response, can I assume the answer is x(t) = 80t, y(t) = 15-16t^2 ?

ddcamp · Answer

Yes

anonymous · Answer

Consider the same ball, same window, same position functions as in the previous question. A ball is thrown straight out at 80 feet per second from an upstairs window that's 15 feet off the ground.? Find the ball's horizontal distance from the window at the moment it strikes the ground.

anonymous · Answer

sqrt.(2h/g) = sqrt.(30/32.154) = 0.966 sec.
(0.966 x 80) = 77.28ft.

anonymous · Answer

My answer is off...?

ddcamp · Answer

Solve for when y(t)=0:
15-16t²=0
t=.968
x(.968)=77.46

anonymous · Answer

Ohhh, I see now. Okay, thanks so much!